Coherent Optical Modems for
Full-Wavefield Lidar

The advent of the digital age has driven the development of coherent optical modems--devices that modulate the amplitude and phase of light in multiple polarization states. These modems transmit data through fiber optic cables that are thousands of kilometers in length at data rates exceeding one terabit per second. This remarkable technology is made possible through near-THz-rate programmable control and sensing of the full optical wavefield. While coherent optical modems form the backbone of telecommunications networks around the world, their extraordinary capabilities also provide unique opportunities for imaging. Here, we repurpose off-the-shelf coherent optical modems to introduce full-wavefield lidar: a type of random modulation continuous wave lidar that simultaneously measures depth, axial velocity, and polarization. We demonstrate this modality by combining a 74 GHz-bandwidth coherent optical modem with free-space coupling optics and scanning mirrors. We develop a time-resolved image formation model for this system and formulate a maximum-likelihood reconstruction algorithm to recover depth, velocity, and polarization information at each scene point from the modem's raw transmitted and received symbols. Compared to existing lidars, full-wavefield lidar promises improved mm-scale ranging accuracy from brief, microsecond exposure times, reliable velocimetry, and robustness to interference from ambient light or other lidar signals.

In a coherent optical modem, binary data are collected and encoded into a discrete sequence of symbols, each paired with a certain amplitude, phase, and polarization state of light (a,b). This sequence of symbols is used to create a piecewise constant waveform with segments of duration 𝑇 (shown for a single polarization). In practice, a band-limited version of this waveform modulates laser light with certain amplitude and optical frequency (c). The modulated light is emitted, collected by the receive port of the modem, and interfered with an unmodulated receiver-side laser to remove the optical frequency shift. The resulting waveform is sampled to recover the demodulated symbols.

In Full-Wavefield Lidar, a modem is used to modulate the output wavefield with predefined symbols. The modulated wavefield is then transmitted to the target through a fiber optic cable, circulator, and collimator. The received wavefield is demodulated and detected by the optical modem to recover the symbols. The transmitted wavefield is distorted by multiple effects: the propagation delay induces a shift in the measurements; scattering off of a moving surface scrambles the two transmitted polarization channels (modeled by multiplication with a Jones matrix R) and induces a Doppler shift; the wavefield is attenuated as it propagates back to the collimator; last, the measurements are corrupted by noise from the optical modem or optical amplifiers. Given the known transmitted symbols and observed received symbols, our maximum-likelihood reconstruction framework then optimizes the depth, velocity and polarization.

The Kinect Azure and single-photon lidars fail at light levels corresponding to 10 𝜇s exposure times (which we emulate using neutral density filters for Kinect, and thinning the detected photon counts for single-photon lidar). On the other hand, Full-Wavefield Lidar recovers accurate depth and velocity with only 1 𝜇s exposure times per pixel and an eye-safe 2 mW laser.

Full-Wavefield Lidar is insensitive to interference from other lidar signals and ambient light. We showcase its insensitivity to strong ambient light by scanning a tungsten halide light bulb while it is turned on. Although the emission spectrum of the bulb includes the 1550 nm wavelength used by the system, FWL reconstructs both the lamp and the highly-specular bulb.

Full-Wavefield Lidar is capable of reconstructing multiple surfaces. We show an example scene where a statuette is placed behind a translucent surface. We recover both surfaces by estimating the time delays of the two reflections with highest power.